Since "laziness is a virtue", I let Tie::File do the file I/O:

#!/usr/bin/perl
use strict;
use warnings;
use Tie::File;
tie my @haiku, 'Tie::File', $0 or die "FOO!";
my $number = 4 * int(rand(@haiku/4 - 2) + 2);
print join "\n", @haiku[$number..$number+3];
__END__
Even in Kyoto
hearing the cuckoo's cry--
I long for Kyoto.
        Basho
In this world
We walk on the roof of hell
Gazing at flowers.
        Issa
The old pond--
a frog jumps in,
sound of water.
        Basho
In the white plum blossoms
night to next day
just turning.
        Buson
Sick on a journey,
my dreams wander
the withered fields.
        Basho
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